®
L a r g e S t r u c t u r e s S e t
B r a c h i s t o c h r o n e
34
Brachistochrone
The word “brachistochrone” is from the Greek words meaning “shortest” (
Βραχιοτοζ
) and “time” (
χρονοζ
).
Imagine two fixed points in a vertical plane so that one of the points is not directly below the other. If a particle
starts from rest at one of the points and descends to the other point under its own weight, the brachistochrone is the
path the particle must take to reach its destination in the briefest time. The brachistochrone may not be the shortest
path, but it is the quickest path..
Set up the structure with two Coaster Tracks side-by-side. Place two Mini Cars at different starting points on the
track and let them go. What happens?
Use cord and Cord Tensioning Clips to cross brace the back of the high end of the ramp.
The brachistochrone curve is part of an
inverted cycloid. A cycloid is the path
of a point that is fixed on the edge of a
circle as the circle rolls along a straight
line.
Imagine a straight ramp and a brachis-
tochrone curve as shown. In a race
from A to B between a ball rolling
down the brachistochrone curve and a
ball rolling down the straight ramp,
which ball will finish first?
#5
#4
#4
#4
#4
#4
#4
#4
#4
#4
#4
#4
Legend:
AC = Angle Connector
CT = Cord Tensioning Clip
F4 = Flat 4 Member
FR = Full Round Connector
FT = Flat Round Connector
HR = Half Round Connector
SL = Sliding Connector
ST = Straight Connector
FR
#1
Flex 5
Flex 4
AC
#2
AC
AC
#3
#3
#1
ST
#6
#5
#4
#6
FR
3 X 4
2 X 3
AC
AC
AC
ST
FR
FT
FT
Figure: Brachistochrone
Cord
CT*
AC
Flex 4
Flex 4
Flex 4
AC
#2
#2
#1
2 X 3
SL
SL
ST
#3
#1
2 X 3
*Do not tighten the
Cord Tensioning Clip
on the cord next to the
finish line. Leave extra
cord so that the cord
can slide through the
clip when the Mini
Cars hit the cord.
SL
See the next page for a
more detailed view of
the ramp structure.
Inverted
cycloid
Point on
circle
Brachistochrone
curve
Ramp
Brachistochrone
curve
A
B
#4
SL
AC
#1
Track
Clip
#3
AC
#5
#6
#6
#5
#5